Answer:
p = 13
Explanation:
When a polynomial f(x) is divided by (x + h) then the remainder is f(- h)
Here both polynomials are divided by (x + 1)
Evaluate them both for x = - 1
3(- 1)³ - 5(- 1)² - 4(- 1) + p, that is
- 3 - 5 + 4 + p
= p - 4 → A
6(- 1)³ + p(- 1)² + 9(- 1) + 5, that is
- 6 + p - 9 + 5
= p - 10 → B
Given that A = 3B, then
p - 4 = 3(p - 10)
p - 4 = 3p - 30 ( subtract 3p from both sides )
- 2p - 4 = - 30 ( add 4 to both sides )
- 2p = - 26 ( divide both sides by - 2 )
p = 13